How smooth is almost every function in a Sobolev space?

Fraysse, Aurélia, and Jaffard, Stéphane. "How smooth is almost every function in a Sobolev space?." Revista Matemática Iberoamericana 22.2 (2006): 663-682. <http://eudml.org/doc/41987>.

@article{Fraysse2006,
abstract = {We show that almost every function (in the sense of prevalence) in a Sobolev space is multifractal: Its regularity changes from point to point; the sets of points with a given Hölder regularity are fractal sets, and we determine their Hausdorff dimension.},
author = {Fraysse, Aurélia, Jaffard, Stéphane},
journal = {Revista Matemática Iberoamericana},
keywords = {Espacios de funciones lineales; Espacios de Sobolev; Espacios de Besov; Continuidad; Regularidad; Fractales; Dimensión de Hausdorff; Ondículas; Sobolev spaces; Besov spaces; prevalence; Haar-null sets; multifractal functions; Hölder regularity; Hausdorff dimension; wavelet bases},
language = {eng},
number = {2},
pages = {663-682},
title = {How smooth is almost every function in a Sobolev space?},
url = {http://eudml.org/doc/41987},
volume = {22},
year = {2006},
}

TY - JOUR
AU - Fraysse, Aurélia
AU - Jaffard, Stéphane
TI - How smooth is almost every function in a Sobolev space?
JO - Revista Matemática Iberoamericana
PY - 2006
VL - 22
IS - 2
SP - 663
EP - 682
AB - We show that almost every function (in the sense of prevalence) in a Sobolev space is multifractal: Its regularity changes from point to point; the sets of points with a given Hölder regularity are fractal sets, and we determine their Hausdorff dimension.
LA - eng
KW - Espacios de funciones lineales; Espacios de Sobolev; Espacios de Besov; Continuidad; Regularidad; Fractales; Dimensión de Hausdorff; Ondículas; Sobolev spaces; Besov spaces; prevalence; Haar-null sets; multifractal functions; Hölder regularity; Hausdorff dimension; wavelet bases
UR - http://eudml.org/doc/41987
ER -